The efficiency of a photochemical reaction is influenced by the wavelength of light used to initiate the reaction. This is because the energy of a photon is inversely proportional to its wavelength, as described by the equation:E = h * c / where E is the energy of the photon, h is Planck's constant 6.626 x 10^-34 Js , c is the speed of light 3.00 x 10^8 m/s , and is the wavelength of the light.In a photochemical reaction, a molecule absorbs a photon and undergoes a chemical change. The efficiency of the reaction depends on the energy of the absorbed photon and the energy required for the reaction to occur. If the photon's energy is too low, the reaction may not proceed, or it may proceed at a slower rate.Now, let's compare the efficiency of a photochemical reaction using light with a wavelength of 400 nm and a wavelength of 500 nm.First, we need to calculate the energy of the photons at each wavelength:E_400 = 6.626 x 10^-34 Js * 3.00 x 10^8 m/s / 400 x 10^-9 m = 4.97 x 10^-19 JE_500 = 6.626 x 10^-34 Js * 3.00 x 10^8 m/s / 500 x 10^-9 m = 3.98 x 10^-19 JAs we can see, the energy of the photon with a wavelength of 400 nm is higher than that of the photon with a wavelength of 500 nm.Now, let's consider a hypothetical photochemical reaction with an activation energy Ea of 4.20 x 10^-19 J. In this case, the photon with a wavelength of 400 nm has enough energy to initiate the reaction, while the photon with a wavelength of 500 nm does not. Therefore, the efficiency of the reaction would be higher when using light with a wavelength of 400 nm.However, it is important to note that this is a simplified example, and the actual efficiency of a photochemical reaction depends on various factors, such as the absorption spectrum of the reactants, the quantum yield of the reaction, and the presence of competing processes. Experimental data would be needed to determine the efficiency of a specific photochemical reaction under different wavelengths of light.